I've never heard of it being done, but logically the mouse would scratch & bite some rather personal areas in a frenzy, before suffocating. It may well want to go in, rather than out

If you had a string tied to it's tail to pull it out, some fur etc would no doubt stay behind.

I've also heard some interesting stories of objects found inside people, from a friend who works in a hospital - none of it sounds fun to me....